the Hadamard Theorem says that any simply connected, complete Riemannian manifold of non-positive sectional curvature is diffeomorphic to $R_{n}$. I know this is a stupid question, but what am I missing here?

  • 2
    $\begingroup$ Hyperbolic space is diffeomorphic to $\mathbb{R}^n$. $\endgroup$ – Max Oct 30 '18 at 15:53
  • $\begingroup$ So that's how it is..I am learning differential geometry by myself, the textbook never mention that. Thanks. $\endgroup$ – knot Oct 30 '18 at 15:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.